Question

a fighter jet descends from an altitude of 800 feet at a rate of 80 feet per minute. the graph of this situation is shown below.
altitude over time
graph: x - axis time (minutes), y - axis altitude (in hundreds of feet), line from (0,8) to (10,0)
what is the zero of this function?
a 10
b 8
c 800
d 80

Explanation:

Step1: Understand the zero of a function

The zero of a function is the input (x - value) when the output (y - value) is 0. In this context, the y - axis represents altitude (in hundreds of feet) and the x - axis represents time (in minutes). We need to find the time (x) when the altitude (y) is 0.

Step2: Analyze the graph

From the graph, we can see that when the altitude (y) is 0 (since the y - axis is altitude in hundreds of feet, y = 0 means 0 feet altitude), the corresponding x - value (time) is 10 minutes. Also, we can verify this using the equation of the line. The initial altitude \(y_0=800\) feet (which is 8 hundred feet, so the y - intercept is 8 when x = 0) and the rate of descent is 80 feet per minute. The equation of the line in slope - intercept form \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. The slope \(m=-\frac{80}{100}=- 0.8\) (since 80 feet per minute is 0.8 hundred feet per minute and it's a descent so negative). The equation is \(y=-0.8x + 8\). To find the zero, set \(y = 0\):
\[

$$\begin{align*} 0&=-0.8x + 8\\ 0.8x&=8\\ x&=\frac{8}{0.8}\\ x& = 10 \end{align*}$$

\]

Answer:

A. 10